English

On Liouville's theorem for the Hessian quotient equation $\sigma_2/\sigma_1$

Analysis of PDEs 2026-02-17 v1

Abstract

We prove Liouville's theorem for semi-convex entire solutions to Hessian quotient equation σ2/σ1=1\sigma_2/\sigma_1=1 in Rn\mathbb{R}^n. The proof is based on the observation that after rewriting the quotient operator as the σ2\sigma_2 operator, acting on a new function, one can refer to the recent result of Shankar and Yuan on Liouville's theorem for σ2\sigma_2 equation.

Keywords

Cite

@article{arxiv.2602.14946,
  title  = {On Liouville's theorem for the Hessian quotient equation $\sigma_2/\sigma_1$},
  author = {Siyuan Lu and Marcin Sroka},
  journal= {arXiv preprint arXiv:2602.14946},
  year   = {2026}
}